Mejia had six points and a nifty assist on Marcus Heard's layup during a 15-6 run that put DePaul (16-11, 7-6 Big East) ahead 59-50 with 5 1/2 minutes left.
DePaul preserved the victory by hitting 14 of 16 free throws -- including a 7-for-8 performance by Burns -- during the final 4 1/2 minutes of play.
McHugh Mattis scored 18 points for South Florida (12-15, 3-10). Kentrell Gransberry had 15 points and seven rebounds.
Mejia had eight points in the first half, helping DePaul take a 29-26 halftime lead. Mattis scored two of his nine points during the opening half on a rebound basket at the buzzer.
The Blue Demons travel to South Bend for a 6 p.m. contest with the Irish on Tuesday, February 20. The game can be seen live on ESPN2 and can be heard on WSCR (670 AM).
Official Box Score
DePaul Wins Third Straight at South Florida
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